Experimentation in Mathematics

Jonathan M. Borwein, David H. Bailey, Roland Girgensohn, David H. Bailey, Jonathan M. Borwein

" ""The authors . . . explain experimental mathematics in a lively, surprisingly accessible fashion. ""-N/ A, L'Enseignement Mathematique , December 2004How large a role will computer computations play in the mathematics of tomorrow? The books under review are about many things, but it is clear that the authors are focused on this question. Their answer: very large. Their attitude: we should embrace this change. -David P. Roberts, MAA Online Read This!, January 2005These are such fun books to read! Actually, calling them books does not do them justice. They have the liveliness and feel of great Web sites, with their bite-size fascinating factoids and their many human- and math-interest stories and other gems. But do not be fooled by the lighthearted, immensely entertaining style. You are going to learn more math (experimental or otherwise) than you ever did from any two single volumes. Not only that, you will learn by osmosis how to become an experimental mathematician. -Doron Zeilberger, American Scientist, March 2005It is impossible to describe the content of the whole work in detail in just a few lines. -Ivan Netuka, EMS, September 2004""Much of the material in the book has arisen from the experiences of the authors while working on a computer based approach to different topics in mathematics. The variety obtained in this way is impressive, the authors have really touched and produced a treasure trove of lovely mathematical gems."" -Fritz Beukers, AMS MathSciNet , May 2005""Mathématiques expérimentales Certains mathématiciens défendent l'idée que les mathématiques sont une science expérimentale: l'ordinateur, dont la puissance de calcul engendre des conjectures, est pour eux une source d’inspiration."" -Jean-Paul Delahaye, Pour la Science--Logic et Calcul, April 2005""Still, experimental mathematics is here to stay. The reader who wants to get an introduction to this exciting approach to doing mathematics can do no better than these books."" -Jeffrey Shallit, Notices of the AMS, September 2005I do not think that I have had the good fortune to read two more entertaining and informative mathematics texts. -Andrew Rechnitzer, Australian Mathematical Society , August 2005""The two books are written in an inviting,conversational, unprepossessing style. They are fascinating as a vast collection of interesting facts, anecdotes, and examples about numbers, primes, polynomials, special functions, definite integrals, series summations, and especially PI."" -Ruben Hersh, SIAM Reviews, January 2006""The two books are written in an inviting, conversational, unprepossessing style. They are fascinating as a vast collection of interesting facts, anecdotes, and examples about numbers, primes, polynomials, special functions, definite integrals, series summations, and especially PI."" -Ruben Hersh, SIAM Reviews, January 2006""Much of the material in the book has arisen from the experiences of the authors while working on a computer based approach to different topics in mathematics. The variety obtained in this way is impressive, the authors have really touched and produced a treasure trove of lovely mathematical gems."" -F. Beukers, Mathematiacl Reviews, April 2005"

• Preface, 1 Sequences, Series, Products and Integrals, 2 Fourier Series and Integrals, 3 Zeta Functions and Multizeta Functions, 4 Partitions and Powers, 5 Primes and Polynomials, 6 The Power of Constructive Proofs II, 7 Numerical Techniques II, Bibliography, Index